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We both grew up in different circumstances and chose distinctive paths. Spending your first few months in care, before being brought up by a Labour-voting mother in a Labour-voting Scottish city isn’t a natural preparation for Tory politics. Likewise, working for a former Tory Cabinet minister in Brussels and rejecting his invitation to follow in his footsteps and ending up standing as a Liberal Democrat in Sheffield instead isn’t exactly an orthodox political path either.

But while we both chose to join different parties — and on many issues have very different views — we share a political passion: education. And we share a vision: a genuinely open society. We are both angered by the scale of inequality and frustrated at the barriers a class-ridden nation places in the way of real social mobility.

Working in coalition gives us both the chance to make the sort of changes that will transform opportunities for all children, especially the most disadvantaged: whether that is the £2.5 billion of extra funding for pupils from poorer homes, a policy worked up in the Liberal Democrat manifesto, or the introduction of free schools, a Conservative commitment.

And both of us agree there is much more to do. Structures developed in the past and attitudes that have grown out of introspective debates need to be challenged. Policy-makers have tended to waste time arguing about when we should select students for particular paths in life instead of giving every child the tools to choose for themself.

At the same time, other nations have raced ahead of us because they have embraced innovation and set the bar higher every year. We have to do the same. That is why we propose to go further and faster in rewarding great teachers, tackling under-performing schools, improving teacher recruitment and modernising our curriculum and examination system.

Our exams in particular need urgent reform. The tests most of our 16-year-olds sit, GCSEs, were designed for an age when most children left school at 16, when only a small minority went to university, when information technology was in its infancy, when the internet was science fiction and when the teaching profession was less prestigious, less well-qualified and less ambitious for every child.

Almost everyone now accepts the problem of grade inflation and, year after year, the dumbing-down debate further chips away at confidence in these exams. Last year the Daily Telegraph revealed how exam boards compete to offer softer courses and easier questions, in a race to the bottom which has narrowed the curriculum, encouraged teaching to the test and sent all the wrong signals to our school leaders.

We have failed to stretch the highest achievers and left lower achievers — still overwhelmingly those from the poorest backgrounds — floundering with grades that many employers consider meaningless. And this year thousands of ordinary students have suffered because the modular design of the English GCSE — linked to the amount of coursework in school — has undermined faith in grading and marking.

So we need new exams for students at the age of 16 — qualifications that are more rigorous and more stretching for the able but which will ensure the majority of children can flourish and achieve their full potential. We will therefore preserve the important concept of a near-universal qualification which gives the same opportunities to students of all abilities.

We believe that if we remove modules and reduce coursework, get rid of the factors that encourage teaching to the test and, above all, ensure there is just one exam board for each subject, we can restore faith in our exams and equip children for the challenges of the 21st century. We will ask exam boards to prepare new tests in English, maths, the sciences, history, geography and languages, drawing on the example of other countries with the best education systems.

We plan to call the new qualifications in these core academic subjects English Baccalaureate Certificates (EBacc) — recognising that they are the foundation on which further study, vocational learning or a satisfying apprenticeship can be built. Success in English, maths, science, a humanities subject and a language will comprise the full English Baccalaureate.

Of course there will be some students who will not sit these exams — the same students who do not sit GCSEs today. We will make special provision for these students, and their schools will be required to produce a detailed record of their achievement in each curriculum area to help them make progress subsequently — and we anticipate some will secure EBacc certificates at the age of 17 or 18.

These reforms are radical — so we will consult widely. Their introduction will require careful preparation. So we propose introducing new English, maths and science certificates in September 2015 with other subjects following.

These changes will also require us to consider afresh how we hold schools accountable, so we will consult widely on a replacement for league tables — we are determined to have better ways of recognising schools that add value and help the poorest.

These reforms have only been made possible because in this Coalition we have been able to be more radical, combining the best ideas and building a consensus broader than either of us could have hoped to on our own. In the battle to make our society more open, mobile and free it has been good to know that by working together we can overcome those forces that have held our children back — the entrenched establishment voices who have become the enemies of promise.